weight painting one side of my model affects the other side in a strange way
You are using x-mirror option:



But, if you name bones correctly,  x-mirror will work for you. You need to name pairs of bone with postfixes ".R" and ".L" like "arm.L" and "arm.R". If you do so, when you will paint weight group "arm.L", "arm.R" will be symmetrical to "arm.L"

Also, learn about rigify